Mortgage curtailment and its roles in mortgage pricing: Theory and estimates

The mortgage prepayment and default options entitle borrowers to choose from four payment alternatives: making the regular payment, completely prepaying the mortgage, defaulting on the mortgage, and curtailing (partially prepaying) the mortgage. Complete prepayment and default have been widely studied in the mortgage valuation literature, while curtailment has been largely ignored, despite the fact that it is common practice among households.; Mortgage curtailment has cash flow magnitude similar to that of default, and it is a very significant risk factor for seasoned mortgages. This dissertation provides theoretical and empirical modeling of mortgage curtailment.; I show that mortgage curtailment is not optimal in a perfect market without transaction costs. The existence of mortgage curtailment is a direct evidence of market imperfection. This dissertation explores the roles of mortgage curtailment in achieving two household's housing finance objectives in an imperfect market: minimizing the value of the mortgage, and achieving optimal leverage.; I first explain mortgage curtailment in a contingent claim framework: curtailment is an embedded option and can be optimally exercised in order to minimize the value of the mortgage when there are transaction costs associated with complete prepayment and/or curtailment. I model the mortgage prepayment option as a compound curtailment option and develop an algorithm to price this option. The advantage of this model over existing prepayment models is that it can determine both when and how much borrowers can be expected to prepay the mortgage. By solving the value of the compound option numerically using a binomial lattice, I show that the mortgage prepayment option can be seriously under-priced without incorporating the option to choose the quantity of prepayment.; In the second theory, I extend previous studies in demand for mortgage debt and show that certain household characteristics and market conditions will influence household's demand for mortgage debt, and further lead to mortgage curtailment.; The empirical part of this study utilizes panel-data techniques and shows that mortgage curtailment is driven by the financial incentives and by the household's desire to re-balance its portfolio, the motivations suggested by the theory.